The study "Mathematical Functions of Form as Tools to Investigate Dendrite Morphology" is now in publishable form. This required the following improvements in the past year. (1.) The function of form, F = (weighted sum of extracellular volume elements within 200 uM of the dendrite) / (volume of dendrite), where the volume elements are weighted by the fraction of synaptic current that reaches the soma, or F = "current gathering capacity over dendrite volume," has now been tested by convincingly optimized model dendrites. The form function of the best of these is no more than 1.4 times that of the best natural dendrites. Thus, as hoped, the best models are better but not by much. This strongly suggests that natural neurons are designed to maximize a function resembling F, and that any shape that maximizes F can be used to model natural dendrites. (2.) For the first time, the branch angles of the model dendrites have been optimized: branches are added sequentially, and each branch goes in a direction that threads the most still empty volume elements. Also, for the first time, the lengths and diameters of all branches have also been individually optimized. (3.) The distribution of optimum branch lengths is surprisingly like those of motoneurons both qualitatively and quantitatively: thick branches are short, thinner higher order branches are longer, and the thinnest branches terminate. The transition to terminating branches occurs when branch diameter falls below about 1.8 uM, as with motoneurons. (4.) When model dendrites have the same ratio "b" of daughter to parent diameter at all branch points, their volume is determined to within 10% by this ratio. The natural value, b = .5 to .75, gives model dendrites in the natural volume range. The need for a particular volume range will be tested in the next paper, as follows. Small dendrites have larger values of F. Thus, if motoneurons wanted to gather maximum current using minimum volume, they would be much smaller and more numerous than they are. If, instead, we postulate that neurons require a certain minimum current capacity to function, we would be able to compute an optimum distribution of dendrite sizes, which can be compared to the natural distribution. We have also started a search for a function of the stepping phase angle that generates good approximations to the variables that can be recorded during locomotion. Orchestrated vectorial fluctuations from the usual configurations can then perhaps be attributed to contributions from other centers in addition to the central pattern generator.